Current and Resistance CHAPTER OUTLINE 27.1 Electric Current 27.2 Resistance 27.4 Resistance and Temperature 27.6 Electrical Power

27.1 Electric Current The current is the rate at which charge flows through this surface If Δ Q is the amount of charge that passes through this area in a time interval Δ t, the average current I av is equal to the charge that passes through A per unit time:

The direction of the current is opposite the direction of flow of electrons

Microscopic Model of Current Consider the current in a conductor of cross-sectional area A. The volume of a section of the conductor of length Δ x is A Δ x. If n represents the number of mobile charge carriers per unit volume (in other words, the charge carrier density), the number of carriers in the gray section is nA Δ x. Therefore, the total charge Δ Q in this section is:

27.2 Resistance The current density J in the conductor is defined as the current per unit area A current density J and an electric field E are established in a conductor whenever a potential difference is maintained across the conductor

SI units of the resistance:

ρ

27.4 Resistance and Temperature Over a limited temperature range, the resistivity of a conductor varies approximately linearly with temperature according to the expression

Resistivity versus temperature for a pure semiconductor, such as silicon or germanium. Resistivity versus temperature for a metal such as copper. The curve is linear over a wide range of temperatures, and ρ increases with increasing temperature. As T approaches absolute zero (inset), the resistivity approaches a finite value ρ0.

Example 27.6 A Platinum Resistance Thermometer

27.6 Electrical Power When I is expressed in amperes, Δ V in volts, and R in ohms, the SI unit of power is the watt

Example 27.7 Power in an Electric Heater